Foams made of amorphous hollow spheres and methods of manufacture thereof

ABSTRACT

Novel cellular solids and foams from amorphous materials with a glass transition temperature (T g ) and methods of forming such materials are provided. In particular, foams are formed by expanding or compressing hollow spheres made of a high strength amorphous material, which is defined as a material having high strength characteristics, but also possessing a glass transition within a confined space. Using such a method, it has been unexpectedly found that it is possible to make cellular structures, including both open and closed cell foams, with customizable properties from materials that have been inaccessible with conventional methods. Moreover, based on calculations high specific strengths and stiffnesses are expected.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional application of and claimspriority to U.S. patent application Ser. No. 13/428,740, filed Mar. 23,2012, now U.S. Pat. No. 9,102,087, entitled “FOAMS MADE OF AMORPHOUSHOLLOW SPHERES AND METHODS OF MANUFACTURE THEREOF,” which claimspriority to U.S. Provisional Patent Application No. 61/466,784, filedMar. 23, 2011, entitled “FOAMING AMORPHOUS HOLLOW SPHERES,” thedisclosures of which are expressly incorporated herein by reference. Thepresent application is also related to U.S. patent application Ser. No.14/790,334, filed Jul. 2, 2015, entitled “FOAMS MADE OF AMORPHOUS HOLLOWSPHERES AND METHODS OF MANUFACTURE THEREOF,” the disclosure of which isexpressly incorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The invention described herein was made in the performance of officialduties by employees of the Department of the Navy and may bemanufactured, used and licensed by or for the United States Governmentfor any governmental purpose without payment of any royalties thereon.This invention (Navy Case 200,253) is assigned to the United StatesGovernment and is available for licensing for commercial purposes.Licensing and technical inquiries may be directed to the TechnologyTransfer Office, Naval Surface Warfare Center Corona.

FIELD OF THE INVENTION

This invention relates generally to novel foams formed of strongamorphous materials, and their method of manufacture; and moreparticularly to a foam formed of a plurality of hollow spheres.

BACKGROUND OF THE INVENTION

Foams and cellular solids are currently used in a wide variety ofcommercial and military applications, including armor, structural loadbearing members, aircraft, cars, thermal and noise insulation, heattransfer, and catalysis. As such, the current state of the art incellular solids is a very broad topic. Research areas include decreasingcosts, increasing strengths, stiffnesses, energy absorption, heatexchange, catalytic capacity, biocompatibility, exploring foamingmethods for new materials, hollow sphere structures, and hightemperature suitable foams. (See, e.g., L P Lefebvre, J Banhart, D CDunand, Adv. Eng. Mat. 10 (2008) 775; Y Boonyongmaneerat, C A Schuh, D CDunand, Scripta Mater. 59 (2008) 336; X Xue, Y Zhao, JOM 63 (2011) 43; ARabiei, L J Vendra, Mater. Lett. 63 (2009) 533; O Reutter, JSauerhering, T Fend, R Pitz-Paal, S Angel, Adv. Eng. Mat. 10 (2008) 812;R Singh, P D Lee, J R Jones, G Poologasundarampillai, T Post, T CLindley, R J Dashwood, Acta Biomater. 6 (2010) 4596; AH Brothers, D CDunand, MRS Bull. 32 (2007) 639; U Jehring, P Quadbeck, H D Böhm, GStephani, in Porous Metals and Metallic Foams, DEStech PublicationsInc., Lancaster, Pa., 2008, pp. 165-168; and Y Boonyongmaneerat, D CDunand, Adv. Eng. Mat. 10 (2008) 379; and G Walther, B Klöden, TWeissgärber, B Kieback, A Böhm, D Naumann, S Saberi, L Timberg in PorousMetals and Metallic Foams, DEStech Publications Inc., Lancaster, Pa.,2008, pp. 125-128, the disclosures of each of which are incorporatedherein by reference.) Aluminum foams dominate the metallic foamliterature and fabrication methods include the use of TiH₂ and CaCO₃blowing agents and modifications to existing methods to achieve betterproperties. (See, L P Lefebvre, (2007), cited above.)

In addition to these standard materials, some research has been done onbonded hollow sphere structures. In conventional techniques, hollowspheres are made by coating sacrificial spheres with crystalline metalsand thermally or chemically removing the sacrificial material oratomizing metallic melts. Hollow crystalline metal spheres can then besintered together or “glued” with a binder material. (See, e.g., W SSanders, L J Gibson, Mat. Sci. Eng. A 347 (2003) 70, the disclosure ofwhich is incorporated herein by reference.) High strength cellularstructures have been achieved with steel alloys (U. Jehring, (2008)cited above) and other crystalline metals (L P Lefebvre, (2007) citedabove), but these individual methods are difficult to engineer, and mayonly be used with a limited number of materials.

As would be understood, regardless of the specific type of foam chosen,the properties required of that foam depend on the particularapplication. For example, foams used for armor and energy absorbingstructures should be as light as possible while absorbing the maximumenergy at a given plateau stress. (See, e.g., M F Ashby, Phil. Trans. R.Soc. A 364 (2006) 15, the disclosure of which is incorporated herein byreference.) In turn, foams used in load bearing applications should bedesigned for minimum weight at a given load. (See, M F Ashby, L UTianjian, Science in China Series B 46 (2003) 521, the disclosure ofwhich is incorporated herein by reference.) Likewise, sandwich panelsand foam core structures (used in aircraft and race cars for example)require maximum stiffness, while minimizing weight. (See, L J Gibson, MF Ashby, Cellular Solids Structure and Properties, Cambridge UniversityPress, New York, N. Y., 1997, pp. 55-61, 345-385, the disclosure ofwhich is incorporated herein by reference.) Meanwhile, closed cell foamscan be used for thermal, vibration, and noise insulation. Open cellfoams, on the other hand, allow exposure to a large surface area tofluids flowing through them, which can be used for heat transfer andcatalysis. (See, M F Ashby, A G Evans, N A Fleck, L J Gibson, J WHutchinson, H N G Wadley, Metal Foams: A Design Guide,Butterworth-Heinemann, Woburn, Mass., 2000, pp. 113-188; and L PLefebvre, J Banhart, D C Dunand, Adv. Eng. Mat. 10 (2008) 775, thedisclosures of which are incorporated herein by reference.)

The general examples above currently require the selection ofappropriate materials for each application, in a time consuming manner.First, the requirements for the application are quantified. Then, a“property profile” is developed which details the characteristics amaterial would need to meet the requirements. This selection processrelies on compendiums of materials to see if a known material matchesthe property profile. If no material exists, new alloys must be inventedor research and development must be performed to address the problem.

Within the amorphous metallic field, many patents on methods for foamingamorphous metallic glasses have been granted. U.S. Pat. No. 5,384,203discusses a method similar to those found in U.S. Pat. Nos. 4,099,961and 5,281,251, wherein a blowing agent is injected into the moltenmixture and the material is foamed above the solidus temperature.Likewise, U.S. Pat. Nos. 7,073,560 and 7,621,314 both teach methods tointroduce blowing agents into the metallic glass forming alloy in themolten state and then expand the bubbles upon cooling from the melt butabove T_(g) or by cooling to a solid, reheating the alloy above T_(g)and expanding the bubbles at that time. Meanwhile, U.S. Pat. No.7,597,840 teaches a method of making a foam precursor by consolidatingamorphous powders around finely dispersed particles of blowing agent andfoaming that mixture above T_(g).

However, despite the extensive research, the scientific literaturereveals limited success in making high porosity foams from metallicglasses. (See, Brothers, Dunand. Scripta Mater. 54 p 513, 2006, thedisclosure of which is incorporated herein by reference.) Expensive Pdand Pt glass forming alloys are one example of high porosity foams.Boron Oxide Hydrate is dissolved in the amorphous melt to form a“pre-foam” and the mixture is expanded at T>T_(g) to form high strength,highly porous structures. (See, Demetriou, Hanan, Veazey, Di Michiel,Lenoir, Ustundag, Johnson. Adv. Mater. 19 p 1957, 2007; and Wang,Demetriou, Schramm, Liaw, Johnson. J. Appl. Phys. 108 p 023505, 2010,the disclosures of which are incorporated herein by reference.) Fe basedmetallic glasses and Zr based metallic glasses have also been foamedusing different methods, but porosity is usually lower than thatobtainable for Pd based bulk metallic glass (BMG) forming alloys. (See,Demetriou, Duan, Veazey, De Blauwe, Johnson. Scripta Mater. 57 p 9,2007; and Brothers, Scheunemann, DeFouw, Dunand. Scripta Mater. 52 p335, 2005, the disclosures of which are incorporated herein byreference.) Nowhere is there provided a method that allows for theformation of foams from a wide-variety of amorphous materials in amanner that also provides a way to uniquely tailor the cell size, wallthickness, internal cell pressure, and material strength.

Accordingly, a need exists to find a novel approach that could producefoams and cellular materials with a range of densities, strengths, andstiffnesses to meet these varied applications and needs.

BRIEF SUMMARY OF THE INVENTION

The current invention is directed generally to foams formed fromamorphous hollow spheres formed from high strength amorphous materials,and methods of their manufacture.

In some embodiments, the invention is directed to a method of forming acellular solid from an amorphous material including:

-   -   obtaining an amorphous material having a glass transition;    -   forming at least one hollow sphere from the amorphous material,        the hollow sphere having an internal pressure;    -   confining the at least one hollow sphere within a body;    -   heating the at least one hollow sphere to a temperature above        the glass transition temperature of the amorphous material;    -   applying a pressure differential between the internal pressure        of the at least one hollow sphere and the pressure of the        atmosphere within the confining body, such that the at least one        hollow sphere one of either expands or contracts within the        boundary defined by the body to form a unitary cellular solid.

In one such embodiment, the method includes a plurality of hollowspheres that expand or contract until they come into contact with anyadjacent hollow spheres.

In another such embodiment, the plurality of hollow spheres bondtogether upon making contact.

In still another such embodiment, the outer surfaces of the plurality ofhollows spheres undergo a surface treatment that enhances the bonding ofspheres at contact points. Such treatments may include but are notlimited to cleaning, etching, exposure to a plasma, and processing ininert atmosphere.

In yet another such embodiment, the plurality of hollow spheres remainunbonded upon making contact.

In still yet another such embodiment, the plurality of hollow spheresundergo a surface treatment to minimize the bonding of spheres atcontact points. Such treatments may include but are not limited toapplications of coatings such as oils, growth of oxides, and exposingthe plurality of spheres to reactive chemicals.

In still yet another such embodiment, the pressure of the atmospherewithin the at least one hollow sphere and the confining body are equalto each other and greater than atmospheric pressure, and the pressuredifferential is generated by depressurizing the atmosphere within theconfining body thereby causing the at least one hollow sphere to expand.

In still yet another such embodiment, the pressure of the atmospherewithin the confining body is greater than the pressure within the atleast one hollow sphere, and wherein the pressure of both are greaterthan atmospheric pressure, and the pressure differential is generated bydepressurizing the atmosphere within the confining body thereby causingthe at least one hollow sphere to expand.

In still yet another such embodiment, the pressure of the atmospherewithin the at least one hollow sphere and the confining body are bothequal to or less than atmospheric pressure, and the pressuredifferential is generated by exposing the atmosphere within theconfining body to a lower pressure thereby causing the at least onehollow sphere to expand.

In still yet another such embodiment, the pressure of the atmospherewithin the at least one hollow sphere is less than the pressure of theatmosphere within the confining body such that when the at least onehollow sphere is heated above the glass transition temperature the atleast one hollow sphere compresses as the pressure within the at leastone hollow sphere and the atmosphere within the confining body movetoward equilibrium.

In still yet another such embodiment, the pressure of the atmospherewithin the at least one hollow sphere is greater than the pressure ofthe atmosphere within the confining body such that when the at least onehollow sphere is heated above the glass transition temperature the atleast one hollow sphere expands as the pressure within the at least onehollow sphere and the atmosphere within the confining body move towardequilibrium.

In still yet another such embodiment, there are a plurality of hollowspheres, and wherein at least two of the spheres have different internalpressures.

In still yet another such embodiment, there are a plurality of hollowspheres, wherein the spheres are formed in at least two sizes.

In still yet another such embodiment, there are a plurality of hollowspheres, wherein the spheres have at least two wall thicknesses.

In still yet another such embodiment, the at least one hollow sphere isformed from a material selected from the group consisting of glasscompositions, silicate glasses, metallic glasses, ceramic glasses, andcomposite materials with an amorphous phase and amorphous or crystallineinclusions.

In still yet another such embodiment, a non-amorphous material isincluded in one of either the inside volume of the at least one hollowsphere or within the confining body.

In still yet another such embodiment, the at least one hollow sphere isexpanded until the sphere ruptures to form an open celled cellularsolid.

In still yet another such embodiment, an open cell cellular solid isformed by minimizing the pressure differential between the internalpressure of the at least one hollow sphere and the pressure of theatmosphere within the confining body such that the hollow spheres areallowed to bond at points of contact.

In still yet another such embodiment, the confining body defines avolume that can one of either expand or compress during the expansion ofthe at least one hollow sphere.

In still yet another such embodiment, the internal volume of the atleast one hollow spheres is filled with a material reactive to theamorphous material.

In still yet another such embodiment, the at least one hollow sphere isformed in an inert atmosphere.

In still yet another such embodiment, at least one hollow sphere has oneof either a positive or negative charge thereon.

In still yet another such embodiment, there are a plurality of chargedhollow spheres, and wherein the spheres are sorted and arranged by meansof their charge within the confining body prior to expansion.

In still yet another such embodiment, further including inserting aductile inclusion within the inner volume of the at least one hollowsphere.

In still yet another such embodiment, the at least one hollow sphere issubmerged in a pressurized fluid and the at least one hollow spherecompressed until the pressure inside the at least one hollow sphereequals the pressure of the fluid to form at least one hollow sphere withan internal pressure greater than the initial pressure.

In still yet another such embodiment, there are a plurality of hollowspheres wherein at least two of the hollow spheres are filled withdifferent gasses.

In still yet another such embodiment, the gas includes one of either aliquid or solid blowing agent.

In still yet another such embodiment, there are a plurality of hollowspheres, and wherein at least two of the hollow spheres are formed ofdifferent amorphous materials.

In other embodiments, the invention is directed to a method of forming acellular solid from an amorphous material including:

-   -   obtaining an amorphous material having a glass transition;    -   forming a plurality of hollow spheres from the amorphous        material, the hollow spheres each having an internal pressure;    -   confining the plurality of hollow spheres within a body;    -   heating the plurality of hollow spheres to a temperature above        the glass transition temperature of the amorphous material; and    -   applying a pressure differential between the internal pressure        of the plurality of hollow spheres and the pressure of the        atmosphere within the confining body, such that the hollow        spheres one of either expand or contract within the boundary        defined by the body until they make contact with at least one        adjacent hollow sphere to form a cellular structure.

BRIEF DESCRIPTION OF THE DRAWINGS

The description will be more fully understood with reference to thefollowing figures and data graphs, which are presented as exemplaryembodiments of the invention and should not be construed as a completerecitation of the scope of the invention, wherein:

FIG. 1, provides a flow chart of an exemplary hollow sphere foamingmethod in accordance with embodiments of the current invention;

FIGS. 2A and 2B provide schematics of foams expected from embodiments ofthe inventive method, including: (A) an open cell foam made of hollowspheres bonded together by pressurizing mold above internal pressure ofspheres and heating to T_(g) where spheres soften and bond together atcontact points, and (B) a closed cell foam made of hollow spheresexpanded by heating material to T_(g) and lowering pressure inside moldbelow pressure inside spheres so spheres expand and bond along faces.

FIGS. 3A and 3B provide schematics of fractal foams in accordance withthe current invention, where: (A) shows a foam formed from three sizesof spheres packed in a square box to make “fractal foam”, and (B) showsthe geometry after the spheres are expanded above T_(g);

FIGS. 4A to 4D provide schematics of techniques of (A-C) injecting acrystalline ductile phase (shown as a dark circle) within the amorphoushollow spheres in accordance with embodiments of the current invention,and (D) forming a armor material out of such a composite material;

FIG. 5, provides a schematic of a hollow sphere foaming process inaccordance with embodiments of the current invention;

FIG. 6 shows a schematic of a method of forming a parabolic mirror formthe expansion of a single hollow sphere in accordance with embodimentsof the current invention;

FIG. 7 shows a schematic of a method of forming a parabolic mirror formthe expansion of a plurality of hollow spheres in accordance withembodiments of the current invention;

FIG. 8 provides plots of theoretical Young's modulus (E*) vs. densityfor hollow sphere foams made of materials with T_(g) (Silicate (E-Glassand S-Glass) and Oxide (B₂O₃) glasses were assumed to be brittle foamswhile BMG and plastic materials were assumed to be plastic foams, φ=0.1is assumed for all spherical foams since most of the volume fraction ofmaterial would be in the faces of the foam), also a comparison ofexperimental data (square points) from (M F Ashby, (2003) cited above)for commercially available aluminum foams and theoretical E* of open andclosed cell aluminum foams (dashed lines) reveals that commerciallyavailable aluminum foams do not attain the theoretical E*; and

FIG. 9 provides plots of theoretical yield strength vs. density forhollow sphere foams made of materials with T_(g). The same assumptionswere made as in FIG. 3. The tensile yield strength of fibers of thebrittle materials is used for the bulk fracture strength. Comparison ofexperimental data (square points) from (M F Ashby, (2003) cited above)for commercially available aluminum foams and theoretical yield strengthof open and closed cell aluminum foams (dashed lines) reveals thatcommercially available aluminum foams do not attain the theoreticalyield strengths. Pressurization of hollow spheres would result inincreases in yield strength.

FIGS. 10A to 10D provide images of cellular foam in accordance withembodiments of the current invention, where: (A) is a picture of thespheres prior to expansion, (B) is a side view of the cylindrical foam,(C) is a top view of a section of the foam, and (D) is a close up viewof (C).

DEFINITIONS OF TERMS

For the purposes of the invention, the terms listed below shall beconsidered to have the following meanings.

Hollow sphere shall mean something that is not necessarily perfectlyspherical, and shall include ellipsoids and other hollow geometries.

The terms BB, microsphere and microballoon shall mean a hollow sphere,without restriction on sphere diameter or wall thickness.

T_(g) shall reference the glass transition temperature of the material.

P_(int) shall reference the pressure inside a hollow sphere.

P_(ext) shall reference the pressure of fluid (gas or liquid) that thesphere resides in (e.g., may be the fluid pressure enclosed within acontainer in which the hollow sphere has been placed).

Surface tension shall reference the surface tension at equilibrium, adroplet with one surface will have a surface tension T given by theequation:P _(int) −P _(ext)=2T/r  (EQ. 1)where r is the radius of the droplet. The pressure differentialsrequired to expand or collapse hollow spheres do not explicitly includesurface tension. Given that surface tension is a function of temperaturefor glasses above T_(g), experimental determination of T(T) would berequired to determine the exact pressures for pressure equilibrium as afunction of temperature.

Container shall mean any shape that prevents infinite expansion ofhollow spheres, e.g., ship hull, airplane wing, a cylinder, a complexshape with internal structure that the foam will fill around.

Foaming shall mean the expansion or contraction of hollow spheres atT>T_(g) due to a pressure differential. For containers filled withhollow spheres, especially multiple sizes, high packing efficiency couldresult and foaming such a structure may involve minimal expansion ofspheres (assuming P_(int)>P_(ext)). Containers partially filled withhollow spheres would likely result in greater expansion of hollowspheres when T>T_(g) (assuming P_(int)>P_(ext)).

Amorphous materials mean a material with a glass transition having bulk(non-porous) material yield strength preferably greater than 500 MPa,more preferably greater than 1000 MPa, and most preferably greater than2000 MPa.

DETAILED DESCRIPTION OF THE INVENTION

The current invention is directed to novel cellular solids and foamsfrom amorphous materials with a glass transition temperature (T_(g)) andmethods of forming such materials. In particular, the current inventionis directed to foams formed by expanding or compressing hollow spheres(made of a high strength amorphous material, which is defined as amaterial having high strength characteristics, but also possessing aglass transition) within a confined space. Using such a method, it hasbeen unexpectedly found that it is possible to make cellular structures,including both open and closed cell foams, with customizable propertiesfrom materials that have been inaccessible with conventional methods.Moreover, based on calculations high specific strengths and stiffnessesare expected.

Embodiments of methods of forming such hollow sphere cellular materialsand foams may follow, for example, the flow chart provided in FIG. 1,which sets out the basic steps of the process, including:

-   -   Selecting a high strength amorphous material;    -   Forming gas-filled hollow spheres from the amorphous material;    -   Enclosing a plurality of the spheres within an enclosed space;        and    -   Either compressing or expanding the spheres to fill the space,        thereby creating the cellular solid or foam desired.        Computer generated images of open cell and closed cell foam        geometries expected from foam embodiments formed from his        fabrication method are shown in FIG. 2. It should be understood        that these images and the final geometries are merely exemplary.        Different final configurations and shapes can be obtained by        modifying the initial pre-expansion packing geometries. For        example, in the example in FIG. 2 cubic close packed spheres        have been expanded forming cells that are rhombic dodecahedrons.

First, with respect to the selection of the material, it should beunderstood that many materials can exist as amorphous solids andtransition from solid-like to liquid-like behavior at a glass transitiontemperature, T_(g), and that so long as these materials have sufficientstrength for engineering applications they are contemplated by thecurrent invention. For the purposes of the instant invention, an“amorphous” material is defined as a substance that behaves like a solidat temperatures where T<T_(g), but softens at temperatures whereT>T_(g). (See, e.g., Busch, Bakke, Johnson. Acta Mater. 46 (13), p 4725,1998, the disclosure of which is incorporated herein by reference.) Somewell-known materials with a T_(g) are listed below, however theinventive process described herein will work with any materialexhibiting a T_(g) and example materials listed in this paragraph aregiven for illustrative purposes only and are not to be considered allinclusive. Materials with T_(g):

-   -   SiO₂ and other glass compositions including borosilicate,        soda-lime, and metal oxide;    -   Metallic glasses including Zr based glasses such as Vitreloy as        well as many other alloy families;    -   Ceramic glasses such as boron oxide, B₂O₃; and    -   Composite materials with an amorphous phase and amorphous or        crystalline inclusions.        It will be noted that this method excludes the possibility of        using plastics or other polymeric materials. The reason for this        exclusion is two-fold, plastics have poor strength and stiffness        characteristics making them unsuitable for the types of        applications contemplated by the instant invention; and plastics        have unique properties that may or may not be analogous to the        techniques contemplated herein. Accordingly, for the purposes of        this application the term amorphous material is defined as        materials having bulk (non-porous) material yield strength        preferably greater than 500 MPa, more preferably greater than        1000 MPa, and most preferably greater than 2000 MPa.

Turning to the method of manufacturing the amorphous hollow spheres. Itwill be understood that amorphous materials can be made into hollowspheres using many different manufacturing routes. For example, an earlymethod for producing hollow spheres from film forming materials wastaught by Kendall et al., which describes a strong instability in thefluid dynamics of annular jets. (See, e.g., J M Kendall, M C Lee, T GWang, J. Vac. Sci. Technol. 20 (1982) 1091; M C Lee, J M Kendall, Appl.Phys. Lett. 40 (1982) 382; and J M Kendall, Proceedings of the SecondInternational Colloquium on Drops and Bubbles (1981) 79, the disclosuresof which are incorporated herein by reference.) In particular, theauthors describe when a gas is flowed coaxially within an annularcylinder of molten material, the material will spontaneously pinch offinto gas filled hollow spheres at 100-1000 Hz. (See, e.g., M C Lee, J MKendall, P A Bahrami, T G Wang, Aerospace America 24 (1986) 72, thedisclosure of which is incorporated herein by reference.)

Further descriptions of suitable techniques are provided in U.S. Pat.No. 2,797,201 (which describe producing hollow spheres from polymerbased materials); U.S. Pat. Nos. 3,615,972 and 3,740,359 which describepolymer or plastic microsphere forming methods); U.S. Pat. No. 2,978,339(which describes a method to produce pressurized hollow glass spheres);and U.S. Pat. No. 4,568,389 (which describes a method for producinghollow metal spheres). The disclosures of all of the references listedin this section are incorporated herein by reference. It should beunderstood that the hollow spheres formed in accordance with thesemethods may have an internal pressure above or below ambient pressure.While, these hollow spheres are often referred to as “BBs”,“microballoons” or “microspheres”, no restriction on the size of thesehollow spheres is given for the purposes of this invention.

Although the above has described the basic methods of manufacturing thehollow spheres, it should be understood that in some embodiments thetechnique may be modified to provide hollow spheres having veryspecifically engineered properties. Some exemplary modificationsinclude:

-   -   A getter may be included (e.g., a hot Ti wire) in an inert        atmosphere where the spheres are formed to minimize the        oxidation of the hollow spheres. This is particularly        advantageous where metallic glass alloy spheres are formed as        oxidation can degrade their properties.    -   Using a method as described above, but with a gas that is        reactive with the material of which the hollow sphere is made so        residual gas will react and be sequestered, leaving the interior        of the sphere at vacuum pressures. Such a technique would be        particularly useful for insulation purposes.    -   Another strategy to prevent oxides or residues from forming or        collecting on the hollow spheres is to form them in an inert        atmosphere and design handling processes and equipment to avoid        exposure to contaminating or reactive atmospheres. One exemplary        technique would be to use a method similar to the one described        above where the falling hollow spheres are contained in a drop        tower filled with inert gas, which could terminate in a glove        box to facilitate removal of hollow spheres from the drop tower.    -   In another embodiment, the hollow metal spheres are either        positively or negatively charged and a charged surface is used        to apply a force on them. Application of either a magnetic field        or an electric field on the charged hollow spheres while in        motion would then act like a mass spectrometer and could allow        the hollow spheres to be sorted and packed in specific        configurations.    -   Using charged spheres it would also be possible to use varying        electric and magnetic fields to selectively stack the hollow        spheres in an ideal packing structure to obtain a “fractal foam”        with multiple sized spheres or in a specific packing structure        for identically sized spheres. (Schematics of such “fractal”        foams can be seen in FIG. 3.) Although one embodiment is shown        in the figures, it should be understood that alternative sphere        size distributions could include ideal aggregate distributions        for dense packing of aggregate as in concrete mixtures.    -   In another alternative for amorphous alloy spheres, ductile        inclusions could be incorporated into the hollow spheres during        manufacture. In such an embodiment, as shown schematically in        FIG. 4a , the droplet (10) of amorphous alloy material would        include an inner stream of a molten alloy that will form a        crystalline inclusion (14) with a lower shear modulus than the        amorphous alloy (12) thus allowing for ductile failure as        described in Hofmann, D. C., et al. Nature, 451: 1085-1089,        (2008), the disclosure of which is incorporated herein by        reference. The inclusion thus formed may fill either the entire        inner volume of the hollow sphere or only a portion thereof (as        shown in FIG. 4b ). Moreover, it is possible to use a foam (16)        of such spheres (FIG. 4c ) to create special composite armor        structures (18), such as, for example, by forming the foam with        bullet tripping geometries to defeat armor piercing bullets        above T_(g) (as shown schematically in FIG. 4d ).    -   Finally, in another embodiment, hollow sphere pressurization can        be done hydrostatically after formation. In such an embodiment,        the sphere would be submerged in a fluid, and the fluid        pressurized above the internal pressure of the hollow sphere.        The liquid and submerged sphere would then be heated to T_(g)        and the sphere shrunk until P_(int)=P_(ext). The material could        then be cooled back to glass at high pressure, or can be further        pressurized at T_(g) to any desired internal pressure. The        advantage of such a technique is that high-pressure hollow        spheres can be formed without the danger of explosive failure        that can occur in the case of hollow spheres pressurized in a        gaseous environment.    -   The gas entrapped within the hollow sphere could be made to vary        depending on the desired properties of the spheres.    -   A liquid or solid blowing agent could be inserted coaxially with        or without the inner fill gas like liquid nitrogen or dry ice,        or liquid/solid Deuterium-Tritium to attain higher hollow sphere        interior pressures and aid in cooling.    -   The hollow sphere could be made in a pressurized and possibly        heated drop tower to allow spheres to be formed with higher        internal pressures

Regardless of the ultimate design and manufacture of the hollow spheres,as long as they are made from an appropriate amorphous material (i.e., ahigh strength material with a glass transition temperature) and placedin a confined space prior to expansion, the method of the invention canbe used to form hollow spheres into a foam cellular structure. Forexample, in some embodiments, one or a plurality of hollow spheres areplaced in a confined region and heated to T_(g) (where the materialsoftens and begins to flow), and then compressed or expanded and bondedtogether by altering the pressure conditions between the chamber or moldin which the spheres are confined and the spheres themselves. Aschematic of this process is provided in FIG. 5. Although this is thesimplest description of the invention possible, it will be understoodthat there are a number of embodiments that allow for the tailoring ofthis method to specific purposes.

In particular, it should be understood that as long as the amorphoushollow spheres are heated above their T_(g) and that a pressuredifferential is applied between the external pressure and internalpressures of the hollow spheres then expansion or compression can beaccomplished. However, the expansion or compression of the hollowspheres may take a number of different forms.

-   -   In one embodiment, hollow spheres (made of amorphous material)        with P_(int)>atmospheric pressure are placed in a pressurized        container (P_(ext)>P_(int)>atmospheric) and heated to T>T_(g).        In such an embodiment the pressurized container is depressurized        and the hollow spheres expand, bond or fuse together.    -   In other embodiments, the hollow spheres (made of amorphous        material) with P_(int)>atmospheric pressure are placed in a        pressurized container (P_(ext)>P_(int)>atmospheric) and heated        to T>T_(g). The pressurized container is depressurized and the        hollow spheres expand, touch each other, and bond or fuse        together.    -   Alternatively, expansion can be obtained where the restriction        P_(int)>atmospheric pressure is removed. In this embodiment,        P_(ext) is decreased below P_(int), both of which are less than        atmospheric pressure after the hollow spheres are heated to a        temperature T>T_(g).    -   In yet another alternative, the hollow spheres could be heated        to T>T_(g) in an environment where P_(ext)<P_(int).    -   In still another alternative, the hollow spheres could be heated        to T>T_(g) in an environment where P_(ext)>P_(int). This would        cause compression of the hollow spheres until P_(int)=P_(ext),        or the temperature dropped below T_(g).

It should be understood that the hollow spheres may be provided withdifferent internal pressures from each other. The advantage of such asystem is that it allows for differential expansion or compression ofspheres based on their variable internal pressures. The internalpressures of the spheres can be measured mechanically if the size andwall thickness and alloy strength are known, otherwise it can bedetermined by lancing the sphere and using P₁V₁=P₂V₂ in gas filledcontainer or increase water pressure method.

The above discussion assumes that the spheres are compressed togethersufficiently to cause bonding of the spheres. It should be understoodthat in any of the above embodiments the spheres might be expanded andheated such that they either fuse together or do not fuse together. Thedetermining factor is the amount of expansion and the extent to whichthe spheres are allowed to intermingle at the low viscosity regime aboveT_(g). In this embodiment, the hollow spheres may not bond, neverthelessany rigidity imparted by filling a container with a pressurized materialthat expands to fill most of the space still provides strength andstiffness to the container greater than would be obtainable in an emptycontainer. In order to maximize the likelihood of expanding hollowspheres not bonding together, surface treatments, such as oxides, oils,or other residues could be used to coat the hollow spheres prior toheating to T>T_(g). By contrast, in order to minimize the likelihood ofexpanding hollow spheres not bonding together, etchants, fluxes, orother surface treatments could be affected to remove unwanted residuesor coatings on the hollow spheres. In one example, spheres could becleaned with a detergent and rinsed prior to heating and foaming. Inanother example, spheres may be cleaned by a plasma. In another examplean etchant such as HF or HCl could be used to remove an oxide layer(especially for Zr or Ti based metallic glasses) and the etchant couldbe evaporated under vacuum at elevated temperatures.

Likewise, in any embodiment, it will be understood that there are anumber of adjustable variables that can be used to engineer theproperties of the final foam, such as, for example, the initial hollowsphere size, the hollow sphere wall thickness, the sphere material, andthe material or lack thereof occupying the center of the hollow sphere.For example, in any embodiment, multiple different sized spheres may bepacked in the container to create a “fractal foam” as described withrespect to FIG. 3, above. Similarly, in any embodiment, the hollowspheres may have differing wall thicknesses to allow for variations inthe material and physical properties of the foams. Finally, in anyembodiment, the hollow spheres may be made of different amorphousmaterials. Moreover, by maintaining proper mass to volume ratios of thehollow spheres, control of “settling” can be achieved prior to thefoaming process allowing for the controlled packing of the sphereswithin the confined spaced. In embodiments where variablewall-thicknesses are desired, the sphere wall thickness can bedetermined by alloy density and weight and diameter measurements.

The above discussion assumes that the only material confined within themold or cellular structure are the amorphous hollow spheres, however, insome embodiments some fraction of the material in the container may benon-amorphous. By including other non-amorphous, and thereforenon-expansive materials within the hollow spheres or simply within theconfining space it is possible to create composite foams withcrystalline, liquid, or gas regions held in place by expanded amorphousmaterial and tunable mechanical properties.

The invention contemplates that some of the hollow spheres may rupturein the foaming process. This can create open cell foams and beneficialpathways of rupture could be designed into the foam if an applicationcalled for such. For example, open foams could be made by raising thetemperature above the glass transition temperature and maintainingP_(int)=P_(ext) without applying other compressive forces. Because thehollow spheres would be allowed time to intermingle at low viscositiesin this scenario, the fusing of the hollow spheres to each other atevery point of contact should be ensured.

The above discussion has focused almost entirely on the design anddisposition of the hollow spheres and the external pressure andtemperature applied to them during expansion of compression, however, itshould be understood that the container in which the spheres are placedcan also be engineered to yield novel foam and cellular structures. Forexample, the container could have movable parts and walls to dynamicallycompress or expand the shape during foaming. One possible beneficialoutcome of releasing pressure of the container in various embodiments ofthis invention is the cooling effect of an expanding gas. This coolingmay allow marginal glass formers to avoid crystallization by quicklycooling them below T_(g) after foaming. The container may also havefixed or removable feed-throughs to make pathways in the foam ifdesired.

Although the above discussion has focused on the process of forming thefoams and cellular solids in accordance with the current invention, itshould be understood that the current invention is also directed to thenovel foams themselves and their applications in a wide variety ofapplications. In particular, because the expansion of the amorphoushollow spheres can take place within any containment vessels of anygeometry, the applications of the foams are unlimited. Moreover, oncethe expansion or compression has taken place, the container wall can beoptionally removed thereby even further expanding the possibleapplications of the foams of the invention. Accordingly, somenon-limiting examples of possible applications include:

-   -   Structural materials and crumple zones for ocean vessel (Naval        or commercial ships), automobile, aircraft, spacecraft, bicycle,        etc.;    -   Filling the inside skin of particular geometries for use as        structural members for load bearing equipment (e.g. rigid        struts, beams, mechanical support equipment or aircraft wings);    -   Packaging materials or crates for the transport/handling of        explosives, rocket motors, and electronic control sections;    -   Energy absorbing structures with possible applications for        explosive/energetic weapons handling, or improvised explosive        device (IED) protection;    -   Flotation;    -   Optical traps;    -   Parabolic mirrors (see FIG. 6 which shows a schematic where a        single hollow sphere of metallic glass or other reflective        amorphous solid is expanded inside a parabolic cavity and then        the front cut-off to allow for reflection off of the interior or        foamed sphere;    -   Parabolic mirrors (see FIG. 7 where the interior of a parabolic        hollow shell is filled with reflective foamed amorphous spheres        to form a reflective surface);    -   Other mirror geometries;    -   Reflectors (tetrahedron/simple cubic geometry/others as        applicable);    -   Thermal/noise insulators (near vacuum in spheres, highly        reflective surfaces);    -   Construction materials (e.g. metallic “wood”, roofing material,        insulation in walls);    -   EMP protection and faraday cage production;    -   X-ray reflection and possible protection for laboratories,        medical facilities, scientists/technicians or medical patients;    -   Electrode construction for batteries and/or fuel cells (the        internal gas could be made to be the fuel/oxidizer for fuel        cells);    -   Using amorphous material with catalytic properties the foams        could be made into catalytic devices (i.e., hollow spheres, made        of metals such as platinum based glasses which have utility as        catalysts, could be used as an open cell foam or have their        densities chosen such that they float in a solution and provide        a large surface area of reaction);    -   Arranging spheres with differing Seebeck coefficients within the        foam could make thermo-electric devices;    -   Arranging spheres with differing electrical resistances could        make 3 dimensional circuit boards and/or electrical devices        (resistors, inductors, capacitors, transistors, switches, to        name a few);    -   Arranging hollow spheres with differing burst characteristics        (wall thickness or internal pressure) a “witness plate” can be        fashioned for measuring high temperatures or high pressures        (i.e., a device to provide a measurement of maximum temperatures        or pressures);    -   Self-sharpening abrasives;    -   Higher density regions such as the edges of a plate or ends or        side of a cylinder could be designed into a foam to allow for        welding or other joining processes of foams to other foams, or        foams to other materials;    -   Various geometries of foam could be brazed or soldered to each        other or other materials with appropriate melting temperature        materials;    -   Hollow spheres filled to high pressures could be used for fuel        storage, for instance hydrogen and oxygen filled spheres could        be used in combustion engines or fuel cells;    -   Unique geometries such as toroids could be linked;    -   Threads of amorphous spheres could be woven;    -   Heat exchanger materials wherein heat from gas, compressed in        spheres deformed by compression, could be removed by a fluid, or        heat could be dissipated from a fluid by gas in spheres cooled        by expanding or removing a force;    -   Mechanical energy storage such as springs including compressive        and extensive and helical or torsional or other geometries;    -   Use of hollow spheres with different coefficients of thermal        expansion arranged to create structures highly tolerant of        temperature fluctuations (useful in gage blocks) (requires        special mold);    -   Variables of wall thickness, internal gas pressure, BB diameter,        composition/yield strength allow different strengths and crumple        zones and directed energy dispersion or failure engineering;    -   Voids may be created by having BBs with higher T_(g) or        non-amorphous material encased in foamed material that are        poured out after foaming;    -   Mold may include internal and external shapes that leave voids        or are left behind which would allow gas/electricity/water paths        to be molded in foam.

EXEMPLARY EMBODIMENTS

The person skilled in the art will recognize that additional embodimentsaccording to the invention are contemplated as being within the scope ofthe foregoing generic disclosure, and no disclaimer is in any wayintended by the foregoing, non-limiting examples.

Example 1 Study of Theoretical Foam Properties

Foam properties naturally depend on the material used, the geometry ofthe foam, the strain rate, and temperature, among other characteristics.However, equations derived for open and closed cell foams with strutsarranged like a cube that describe the basic properties have somesimilarities and can be used to provide some theoretical limits on theproperties of the foams of the instant invention. (See, L G Gibson(1997) cited above.) First, the Young's modulus of foams is mostgenerally described by EQ 2 below:

$\begin{matrix}{\frac{E^{*}}{E_{s}} \approx {{\varphi^{2}\left( \frac{\rho^{*}}{\rho_{s}} \right)}^{2} + {\left( {1 - \varphi} \right)\frac{\rho^{*}}{\rho_{s}}} + \frac{P_{internal}\left( {1 - {2v^{*}}} \right)}{E_{s}\left( {1 - \frac{\rho^{*}}{\rho_{s}}} \right)}}} & \left( {{EQ}.\mspace{14mu} 2} \right)\end{matrix}$All terms are used for closed cell foams, but the internal pressurevariable is not used for open cell foams. The final term accounts forinternal cell pressure (notice that the stiffness of the foam willincrease as the internal bubble pressure increases). With regard to theother terms, E* and E_(s) are the Young's modulus of the foam and thebulk solid respectively, φ is the volume fraction of material containedin the cell edges, ρ* and ρ_(s) are the density of the foam and bulksolid respectively, P_(internal) is the internal pressure of a cell, andν*≈⅓ is the Poisson ratio of the foam.

The first term of EQ. 3 reveals a quadratic dependence of Young'smodulus in open cell foams on relative density (ρ*/ρ_(s)). This causesdramatic decreases in specific stiffness as relative density isdecreased. Closed cell foams with a large volume fraction of material incell faces have φ<<1. This leads to the quadratic term approaching zero.Closed cell foams should show a nearly linear dependence on relativedensity due to the second term of EQ. 2. This stiffness is not reachedin practice due to foam defects. Certain geometries of cellularstructures (e.g. out of plane loaded honeycombs) also have lineardependence on ρ*/ρ_(s).

Using the foam fabrication method in this proposal, open cell structureswould consist of spherical closed cells bonded together at contactpoints. This geometry creates channels of access to the foams highsurface area while maintaining much of the stiffness and strength ofclosed cell foams. (See, W S Sanders, L J Gibson, Mat. Sci. Eng. A 347(2003) 70, the disclosure of which is incorporated herein by reference.)FIG. 8 shows theoretical Young's modulus versus density plots of hollowsphere amorphous foams compared to theoretical Young's modulus of closedand open cell aluminum foam. This is overlaid with experimental datafrom commercially available aluminum foams taken from Ashby's MetalFoams: A Survey. (M F Ashby (2003) cited above.)

Closed cell foams are also higher than open cell foams as seen in EQ. 3.As with EQ. 2, the second linear term dominates the yield strength inclosed cell foams.

$\begin{matrix}{\frac{\sigma^{*}}{\sigma_{ys}} = {{A*\left( {\varphi*\frac{\rho^{*}}{\rho_{s}}} \right)^{3/2}} + {B*\left( {1 - \varphi} \right)\frac{\rho^{*}}{\rho_{s}}} + \frac{P_{internal} - P_{{at}\; m}}{\sigma_{ys}}}} & \left( {{EQ}.\mspace{14mu} 3} \right)\end{matrix}$Again, all terms are used for closed cell foams, but the internalpressure terms are not used for open cell foams. The final term accountsfor internal cell pressure (notice that the strength of the foam willincrease as the internal bubble pressure increases). With regard to theother terms, σ* and σ_(ys) are the yield fracture stress of the foam andbulk solid respectively, A≈0.3 for foams made of material that yieldsplastically (A≈0.2 for brittle foams), B≈0.4 for foams made of materialthat yields plastically (B≈1 for brittle foams) (see, L J Gibson, (1997)cited above), P_(atm) is the external or atmospheric pressure, and theother variable are as defined before.

A hollow sphere has a maximum internal pressure it can withstand beforerupturing. This pressure can be estimated by using a result from thinwall pressure vessel theory and an approximation of the relative densityof a thin wall hollow sphere, as follows:

-   -   Pressure vessel equation:

$\sigma = \frac{\Pr}{2t}$

-   -   Relative density equation:

$\frac{\rho^{*}}{\rho_{s}} = \frac{3t}{r}$where P is the internal pressure, r is the radius and t is the thicknesswith other variables defined as above. Combining these two equations andsetting σ=σ_(ys) gives:

$\begin{matrix}{P_{m\;{ax}} = {\frac{2}{3}\frac{\rho^{*}}{\rho_{s}}\sigma_{ys}}} & \left( {{EQ}.\mspace{14mu} 4} \right)\end{matrix}$

Inserting this result into EQ. 3 and assuming P_(max) is much greaterthan P_(atm) approximates the maximum relative strength achievable for agiven relative density for a given material in accordance with:

$\begin{matrix}{\frac{\sigma^{*}}{\sigma_{ys}} = {{A*\left( {\varphi*\frac{\rho^{*}}{\rho_{s}}} \right)^{3/2}} + {B*\left( {1 - \varphi} \right)\frac{\rho^{*}}{\rho_{s}}} + {\frac{2}{3}\frac{\rho^{*}}{\rho_{s}}}}} & \left( {{EQ}.\mspace{14mu} 5} \right)\end{matrix}$

Closed cell foams with a high volume fraction of material in the cellfaces have a linear dependence on relative density as opposed to the 3/2power dependence of open cell foams [See, L J Gibson, (1997) citedabove]. Depending on cellular solid geometry, other relative densityexponential dependencies exist. Packing spheres into specific cellulargeometries may allow further tailoring of foam properties. (See, W SSanders, L J Gibson, Mat. Sci. Eng. A 352 (2003) 150, the disclosure ofwhich is incorporated herein by reference.)

Bulk oxide, silicate, and metallic glasses are known for brittlefracture. Weibull statistics describe the scatter in failure stresses ofbrittle materials by assuming a critical flaw distribution. Thin walledsections and small diameter fibers exhibit high yield strengths due tothe low probability of a critical flaw existing in the volume. (See, Y YZhao, Evan Ma, J Xu, Scripta Mater. 58 (2008) 496, the disclosure ofwhich is incorporated herein by reference.) In the case of metallicglasses, high compressive and bending plasticity evidenced by shearbands has been observed. (See, R D Conner, W L Johnson, N E Paton, W DNix, J. Appl. Phys 94 (2003) 904, the disclosure of which isincorporated herein by reference.) The internal cell pressurization termin EQ. 2 is negligible for pressures up to 10% of the burst strength ofhollow spheres assuming thin wall pressure vessel theory, but makes alarger contribution toward yield strength in EQ 3.

FIG. 9 shows theoretical yield/fracture stress vs. density plots ofhollow sphere foams compared to theoretical yield stress of closed andopen cell aluminum foam. This is overlaid with experimental data fromcommercially available aluminum foams taken from. (See, M F Ashby,(2003) cited above.)

These calculations indicate that foams and cellular solids made with theproposed method will achieve theoretical strengths and stiffnesses thatare greatly improved over conventional materials. As shown, one end ofthe spectrum is occupied by stochastic foams plagued by uneven cellsizes and wall thicknesses due to the conventional manufacturing methodsinvolving dissolved blowing agents or injection of gasses into moltenmaterial. (See, L P Lefebvre, (2008) cited above.) Cellular solids madeby bonding corrugated sheets or constructed from intricate wire or strutgeometries are far more regular and can approach theoretical properties.(See, L J Gibson, (1997) cited above.) The proposed method will likelymirror the predictable properties of engineered cellular structures andhave very uniform cell sizes due to the high uniformity and surfacequality of the hollow spheres. (See, W S Sanders, (2003), cited above.)Spheres with diameters from 50 μm to 4 mm have been fabricated with themethod described in U.S. Pat. No. 4,568,389 (the disclosure of which isincorporated herein by reference), however, not at the temperatures,pressures, or with the materials discussed in this disclosure. Theproposed method would allow foams to be created with close packinggeometries like HCP (Hexagonal Closed Pack) or FCC (Face Centered Cubic)with identical spheres, and higher packing efficiency could be achievedby using multiple sphere sizes. If desired, more open cellular structuregeometries could be constructed and random packing of spheres could alsobe explored.

Example 2 Exemplary Hollow Sphere Cellular Solid

To prove the efficacy of the technique, hollow spheres of silicate glasswere placed in a sealed quartz tube and heated to 1100 C for 1 hour tocreate the foam seen in FIGS. 10a-10d . The foam dimensions are 4 mmdiameter by 25 mm long.

CONCLUSION

Many foam making methods are highly specialized and applicable to only asmall class of materials such as use of titanium hydride (TiH₂) orcalcium carbonate (CaCO₃) to foam aluminum alloys. The versatility ofthe method proposed herein arises from the many variables that can bealtered, such as for example,

-   -   by altering the material (with T_(g)) from which the hollow        spheres are made from,    -   by altering the fabrication of the hollow spheres to vary their        wall thickness or diameter,    -   by altering to control the amount of compression or expansion of        the spheres at T_(g),    -   by altering the packing geometry of the spheres, and    -   by altering the composition of the sphere's internal void.

The versatility of this method should enable fabrication of cellularstructures and foams with open or closed cell geometries that far exceedspecific strengths and moduli of currently available cellular materials.This is due to the high specific strengths and moduli of many amorphousmaterials and the dependence of foams on the properties of the parentmaterial. Calculations of theoretical strengths and stiffnesses of foamsmade with this method exceed currently available metal foams by as muchas two orders of magnitude. Moreover, cellular structures made from awide variety of materials, including, silicate glass, metallic glass andoxide glasses should be achievable using this method.

DOCTRINE OF EQUIVALENTS

Those skilled in the art will appreciate that the foregoing examples anddescriptions of various preferred embodiments of the present inventionare merely illustrative of the invention as a whole, and that variationsin the steps and various components of the present invention may be madewithin the spirit and scope of the invention. For example, it will beclear to one skilled in the art that additional processing steps oralternative configurations would not affect the improved properties ofthe foams and methods of manufacture of the current invention nor renderthe method/foams unsuitable for its intended purpose. Accordingly, thepresent invention is not limited to the specific embodiments describedherein but, rather, is defined by the scope of the appended claims.

What is claimed is:
 1. A method of forming a cellular solid from anamorphous material comprising, obtaining an amorphous materialexhibiting a glass transition at a glass transition temperature, andhaving a material yield strength greater than 500 MPa; forming aplurality of hollow spheres wherein at least the outer surface of thesphere is formed from the amorphous material, the hollow spheres eachhaving an internal pressure; confining the hollow spheres within aconfining body having a fixed volume and having an atmosphere; heatingthe plurality of hollow spheres to a temperature above the glasstransition temperature of the amorphous material; and applying apressure differential between the internal pressures of the plurality ofhollow spheres and the pressure of the atmosphere within the confiningbody, wherein the internal pressures of the plurality of hollow spheresis higher than the pressure of the atmosphere within the confining bodysuch that the plurality of hollow spheres undergo an expansion withinthe boundary defined by the confining body such that adjacent hollowspheres make contact to form a cellular solid.
 2. The method of claim 1,wherein the plurality of hollow spheres expand until the spaces betweenthe adjacent hollow spheres are entirely closed.
 3. The method of claim1, wherein the plurality of hollow spheres bond together upon makingcontact.
 4. The method of claim 3, wherein the outer surfaces of theplurality of hollow spheres undergo a surface treatment that enhancesthe bonding of spheres at contact points.
 5. The method of claim 4,wherein the surface treatment is selected from the group consisting ofcleaning, etching, exposure to a plasma and processing in inertatmosphere.
 6. The method of claim 1, wherein the internal pressureswithin the plurality of hollow spheres and the pressure of theatmosphere within the confining body are equal to each other and greaterthan atmospheric pressure, and the pressure differential is generated bydepressurizing the atmosphere within the confining body thereby causingthe plurality of hollow spheres to expand.
 7. The method of claim 1,wherein the pressure of the atmosphere within the confining body isgreater than the internal pressures within the plurality of hollowspheres, and wherein the pressure of both are greater than atmosphericpressure, and the pressure differential is generated by depressurizingthe atmosphere within the confining body thereby causing the pluralityof hollow spheres to expand.
 8. The method of claim 1, wherein theinternal pressures within the plurality of hollow spheres and thepressure of the atmosphere within the confining body are both equal toor less than atmospheric pressure, and the pressure differential isgenerated by exposing the atmosphere within the confining body to alower pressure thereby causing the plurality of hollow spheres toexpand.
 9. The method of claim 1, wherein the internal pressures withinthe plurality of hollow spheres is greater than the pressure of theatmosphere within the confining body such that when the plurality ofhollow spheres are heated above the glass transition temperature theplurality of hollow spheres expand as the internal pressure within theplurality of hollow spheres and the atmosphere within the confining bodymove toward equilibrium.
 10. The method of claim 1, wherein at least twoof the plurality of hollow spheres have different internal pressures.11. The method of claim 1, wherein at least two of the plurality ofhollow spheres are formed in at least two sizes.
 12. The method of claim1, wherein at least two of the plurality of hollow spheres have at leasttwo wall thicknesses.
 13. The method of claim 1, wherein a non-amorphousmaterial is included in one of either the inside volume of the pluralityof hollow spheres or within the confining body.
 14. The method of claim1, wherein the internal volume of the plurality of hollow spheres arefilled with a material reactive to the amorphous material.
 15. Themethod of claim 1, wherein the plurality of hollow spheres are formed inan inert atmosphere.
 16. The method of claim 1, wherein at least one ofthe plurality of hollow spheres has one of either a positive or negativecharge thereon.
 17. The method of claim 1, wherein the plurality ofhollow spheres are sorted and arranged within the confining body priorto expansion.
 18. The method of claim 1, further comprising inserting aductile inclusion within the internal volumes of the plurality of hollowspheres.
 19. The method of claim 1, wherein the plurality of hollowspheres are submerged in a pressurized fluid and the plurality of hollowspheres compressed until the internal pressures of the plurality ofhollow spheres equals the pressure of the fluid such that the pluralityof hollow spheres have internal pressures greater than the initialpressure.
 20. The method of claim 1, wherein at least two of theplurality of hollow spheres are filled with different gasses.
 21. Themethod of claim 1, wherein at least two of the plurality of hollowspheres are formed of different amorphous materials.
 22. The method ofclaim 1, wherein the plurality of hollow spheres include one of either aliquid or solid blowing agent.